"Math and Genetic Tests"
Reading this article about a possible genetic test for extreme longevity mostly makes me think that if we’re going to have widespread genetic testing in the future, we’re going to need to do a better job of getting people to write about statistical issues clearly:
When it becomes affordable to have one’s genome sequenced, perhaps in a few years, a longevity test, though not a foolproof one, may be feasible, if a new claim holds up. Scientists studying the genomes of centenarians in New England say they have identified a set of genetic variants that predicts extreme longevity with 77 percent accuracy.
So if I get the test and the test comes out positive, does that mean I have a 77 percent chance of living an extremely long time? I’m not totally certain. Later the article explains that “[s]ome 15 percent of his control group, and presumably of the population at large, have the potential to live to be 100.” So one way to interpret the article is saying that there’s a 15 percent chance any given person has longevity genes, and the test for longevity genes is 77 percent accurate, then if you test everyone about 20 percent of the population (.23*.85=.2025) will be false positives, and only 12 percent (.77*.85=.1155) will be accurate positives.
I’m not certain that’s the right way to interpret the article, but I think that’s what it’s saying. The moral of the story, however, is that if you test people randomly for rare conditions then even accurate tests will reveal more false positives than real positives. That doesn’t necessarily mean such tests aren’t worth doing in some situations, but it’s going to be important to make sure that people understand how the odds work in these kind of situations.
Update from Ryan: Doing a quick Bayesian analysis, it seems like if an individual person tests positive, that person actually only has a 37% chance of living longer. As Matt says, does that really tell you very much? You would still have basically a 2/3 chance of not having increased longevity even after a positive test result. Please fix my math in comments if it’s incorrect!